Answer:
B.
Step-by-step explanation:
First, note that since [tex]sin(\theta)=2/3[/tex], this means that the opposite side is 2, the hypotenuse is 3, and the last, adjacent side is [tex]\sqrt{5\\[/tex].
Also note that we are told that [tex]sec(\theta)<0[/tex]. This means that [tex]\theta[/tex] cannot be in quadrants 1 nor 4 because (remember All Students Take Calculus?) in those quadrants cosine and secant are positive. Also, we know that sine is positive so we can conclude that [tex]\theta[/tex] is in the second quadrant.
In the second quadrant, sine is positive, cosine is negative, and tangent is negative. Now we can answer the question. We already know the side lengths: opposite=2, adjacent=[tex]-\sqrt{5}[/tex] (because it's in Quadrant II), and hypotenuse=3.
Therefore...
[tex]cos(\theta)=-\sqrt{5} /3[/tex]
[tex]tan(\theta)=2/(-\sqrt{5})=-(2\sqrt{5}/5)[/tex]
